The perimeter of a right triangle is 2+ 6. If the length of the center line on the hypotenuse is 1, the area of the triangle is equal to () A. 1 B. 1 two C. 1 four D. 3 four

The perimeter of a right triangle is 2+ 6. If the length of the center line on the hypotenuse is 1, the area of the triangle is equal to () A. 1 B. 1 two C. 1 four D. 3 four

∵ CD is the center line on the hypotenuse of right triangle ABC,
∴AB=2CD=2，
∵ the perimeter of right triangle ABC is 2+
6，
∴AC+BC=
6，
Square of both sides: ac2 + 2Ac • BC + BC2 = 6,
From Pythagorean theorem: ac2 + BC2 = AB2 = 4,
∴2AC•BC=2，
AC × BC=1，
∴S△ABC=1
2AC × BC=1
21=1
2．
Therefore, B

The perimeter of a right triangle is 30 and the length of the center line on the hypotenuse is 6.5. Find the area of the right triangle To the process

Assuming that the side lengths of the two right angles are x, y and the length of the hypotenuse is Z, then x + y + Z = 30. According to "the center line on the hypotenuse of the right triangle is equal to half of the hypotenuse", z = 6.5 * 2 = 13, then x + y = 30-z = 17, then x = 17-y. because the triangle is a right angle triangle, the square of X + the square of y = the square of Z, that is, the square of (17-y) + the square of y =

If the perimeter of a right triangle is 28 and the center line on the hypotenuse is 5, the area of this right triangle is

The length of the center line is 5, indicating that the sum of the hypotenuse and the right angle is 28-10 = 18
OK, let's assume that a right angle side is a and a right angle side is B
（A+B)^2=18^2=324
That is, a ^ 2 + B ^ 2 + 2Ab = 324
And a ^ 2 + B ^ 2 = 10 ^ 2 = 100 (Pythagorean theorem)
So 2Ab = 224
So AB = 112
AB/2=56
So the area of the triangle is 56

If the perimeter of a right triangle is equal to 24cm and the length of the center line on the hypotenuse is 5cm, the area of this triangle is equal to __

∵ CD is the center line on the hypotenuse of right triangle ABC,
∴AB=2CD=10，
∵ the perimeter of right triangle ABC is 24,
∴AC+BC=14，
Square of both sides: ac2 + 2Ac • BC + BC2 = 196,
From Pythagorean theorem: ac2 + BC2 = AB2 = 100,
∴2AC•BC=96，
AC × BC=48，
∴S△ABC=1
2AC × BC=1
two × 48=24．
So the answer is 24cm2

The circumference of a right triangle is 36 cm, and the length ratio of the three sides is 3:4:5. How many square centimeters is the area of this triangle?

36÷﹙3＋4＋5﹚=3
three × 3=9
three × 4=12
His area= ½× nine × 12=54 ㎝ ²

If the ratio of three sides of the triangle is 3:4:5 and the perimeter is 24, the area of the triangle is __

Let the three sides of the triangle be 3x, 4x and 5x, then 3x + 4x + 5x = 24, and the solution is x = 2
The three sides of the triangle are 6, 8 and 10
‡ area of triangle = 1
two × six × 8=24